You can run openclaw locally against ollama if you want. But the models that are distilled/quantized enough to run on consumer hardware can have considerably poorer quality than full models.
You need very high-end hardware to run the largest SOTA open models at reasonable latency for real-time use. The minimum requirements are quite low, but then responses will be much slower and your agent won't be able to browse the web or use many external services.
I see mentions of Claude and I assume all of these tools connect to a third party LLM api. I wish these could be run locally too.